#include <bits/stdc++.h>
#define int long long
using namespace std;

const int N = 1000010;
int T, cnt, ans, sum;
string s;
stack <char> stk;

int sp(char x) {
    if (x != '(' && x != ')' && x != '[' && x != ']' && x != '{' && x != '}' && x != '<' && x != '>') return 1;
    return 0;
}

int z(char x) {
    if (x == '(' || x == '[' || x == '{' || x == '<') return 1;
    return 0;
}

int ck(char x, char y) {
    if (sp(x)) return 2;
    if (sp(y)) return 3;
    if (x == '(') {
        if (y == ')') return 1;
        else {
            if (y == ']' || y == '}' || y == '>') return 0;
            return 4;
        }
    } else if (x == '[') {
        if (y == ']') return 1;
        else {
            if (y == ')' || y == '}' || y == '>') return 0;
            return 4;
        }
    } else if (x == '{') {
        if (y == '}') return 1;
        else {
            if (y == ')' || y == ']' || y == '>') return 0;
            return 4;
        }
    } else if (x == '<') {
        if (y == '>') return 1;
        else {
            if (y == ')' || y == ']' || y == '}') return 0;
            return 4;
        }
    }
    return 4;
}

signed main() {
    freopen("kakko.in", "r", stdin);
    freopen("kakko.out", "w", stdout);
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    cin >> T;
    while (T--) {
        cin >> s;
        cnt = 0, ans = 0, sum = 0;
        while (!stk.empty()) stk.pop();
        for (int i = 0; i <= s.size(); i++) {
            if (i == s.size()) {
                if (stk.size()) {
                    cout << "FALSE\n";
                    break;
                }
                cout << "TRUE " << ans << " " << sum << "\n";
                break;
            }
            if (stk.empty()) {
                if (z(s[i]) == 0) {
                    cout << "FALSE\n";
                    break;
                }
                stk.push(s[i]);
                cnt++;
                if (cnt == ans) sum++;
                if (cnt > ans) {
                    ans = cnt;
                    sum = 1;
                }
                continue;
            }
            char a = stk.top();
            stk.push(s[i]);
            if (ck(a, s[i]) == 1) {
                stk.pop();
                stk.pop();
                cnt--;
            } else if (ck(a, s[i]) == 0) {
                cout << "FALSE\n";
                break;
            } else if (ck(a, s[i]) == 2) {
                continue;
            } else if (ck(a, s[i]) == 3) {
                continue;
            } else {
                if (z(s[i]));
                cnt++;
                if (cnt == ans) sum++;
                if (cnt > ans) {
                    ans = cnt;
                    sum = 1;
                }
            }
        }
    }
    return 0;
}